On one empirical model of nonlinear deformation of elastoplastic materials

Abstract

The idea develops that at different sections of the strain-stress curve, the elastoplastic properties of materials are determined by different deformation mechanisms and are described by different relations between strain and stress. Nonlinear strain-stress model of plastic material without hardening is considered, for which existence of two fundamentally different sections of non-zero length on strain-stress curve is postulated. The first section corresponds to Hooke's linear law. The boundary of the first is the point of the proportionality limit. The plastic deformation section begins behind this point and ends with another characteristic point of the strain-stress curve - the point of ultimate strength. In the second section of the strain-stress curve, the relationship between strain and stress is determined by power law. Using the example of a sample of 30 experimental points of the steel deformation curve, an engineering deformation curve corresponding to the formulated law 20ХГР constructed. Experimental data are processed using the standard least squares method. To accelerate the search for extreme point coordinates in a two-dimensional area, the compression operator method is used. The standard deviation for the proposed empirical law from the corresponding sample of experimental points was $S_0=0.02$. The obtained accuracy allows using the formulated empirical model in practical engineering calculations.